This paper presents a method for designing and quantifying the performance of feedback stochastic controls for nonlinear systems. The design makes use of the method of stochastic averaging to reduce the dimension of the state space and to derive the Ito^ stochastic differential equation for the response amplitude process. The moment equation of the amplitude process closed by the Rayleigh approximation is used as a means to characterize the transient performance of the feedback control. The steady state and transient response of the amplitude process are used as the design criteria for choosing the feedback control gains. Numerical examples are studied to demonstrate the performance of the control.
A Stochastic Averaging Approach for Feedback Control Design of Nonlinear Systems Under Random Excitations
Contributed by the Technical Committee on Vibration and Sound for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received Aug. 2001; Revised May 2002. Associate Editor: R. Ohayou.
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Elbeyli , O., and Sun, J. Q. (September 20, 2002). "A Stochastic Averaging Approach for Feedback Control Design of Nonlinear Systems Under Random Excitations ." ASME. J. Vib. Acoust. October 2002; 124(4): 561–565. https://doi.org/10.1115/1.1501084
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